While having diarrhea, you take a shit on someone's chest (preferably a female so the breasts are utilized as a canal) and then the person stands up. Allowing the runny defecate to act as a mudslide, running down the torso.
I was on a cheap domestic beer binge and your mom let me demonstrate a Bavarian Mudslide on her for the party entertainment.
When you shit on her back, then run at her and put your legs up to let your dick get in dat ass.
Yo, my bitch was sittin' on da bed last night, so I did a Nigerian Mudslide on her ass.